We study the process $e^+e^-to J/psipi^{+}pi^{-}$ with initial-state-radiation events produced at the PEP-II asymmetric-energy collider. The data were recorded with the BaBar detector at center-of-mass energies 10.58 and 10.54 GeV, and correspond to an integrated luminosity of 454 $mathrm{fb^{-1}}$. We investigate the $J/psi pi^{+}pi^{-}$ mass distribution in the region from 3.5 to 5.5 $mathrm{GeV/c^{2}}$. Below 3.7 $mathrm{GeV/c^{2}}$ the $psi(2S)$ signal dominates, and above 4 $mathrm{GeV/c^{2}}$ there is a significant peak due to the Y(4260). A fit to the data in the range 3.74 -- 5.50 $mathrm{GeV/c^{2}}$ yields a mass value $4244 pm 5$ (stat) $ pm 4$ (syst)$mathrm{MeV/c^{2}}$ and a width value $114 ^{+16}_{-15}$ (stat)$ pm 7$(syst)$mathrm{MeV}$ for this state. We do not confirm the report from the Belle collaboration of a broad structure at 4.01 $mathrm{GeV/c^{2}}$. In addition, we investigate the $pi^{+}pi^{-}$ system which results from Y(4260) decay.